[SciPy-User] simplex algorithm and curve fitting

[josef.pktd at gmail.com]

On Tue, Feb 21, 2012 at 4:38 AM, servant mathieu
<servant.mathieu at gmail.com> wrote:
> Dear Scipy users,
>
> I've got some troubles with the scipy.optimize.curve_fit function. This
> function is based on the Levenburg-Maquardt algorithm, which is extremely
> rapid but usually finds a local minimum, not a global one (and thus often
> returns anormal parameter values). In my research field, we usually use
> Nelder Mead's simplex routines to avoid this problem. However, I don't know
> if it is possible to perform curve fitting in scipy using simplex; the fmin
> function  doesn't seem to perform adjustments to data.
>
> Here is my code for fitting a three parameters hyperbolic cotangent function
> using curve_fit:
>
> from scipy.optimize import curve_fit
>
> import numpy as np
>
>
>
> def func (x, A,k, r ):
>
> return r + (A /(k*x)) * np.tanh (A*k*x)
>
>
>
> xdata = np.array ([0.15,0.25,0.35,0.45, 0.55, 0.75])
>
>
>
> datacomp = np.array ([344.3276300, 324.0051063, 314.2693475,
> 309.9906375,309.9251162, 307.3955800])
>
> dataincomp = np.array ([363.3839888, 343.5735787, 334.6013375, 327.7868238,
> 329.4642550, 328.0667050])
>
>
>
> poptcomp, pcovcomp = curve_fit (func, xdata, datacomp, maxfev = 10000)
>
> poptincomp, pcovincomp = curve_fit (func, xdata, dataincomp, maxfev = 10000)
>
>
>
>
>
> How could I proceed to perform the fitting using simplex?

You need to define your own loss function for the optimizers like
fmin, or in future version minimize
http://docs.scipy.org/doc/scipy-0.10.0/reference/tutorial/optimize.html#nelder-mead-simplex-algorithm-fmin

something like this

def loss(params, args)
     A, k, r = params
     y, x = args
     return ((y - func (x, A,k, r ))**2).sum()

and use loss in the call to fmin

Josef

>
>
>
> Best,
>
> Mat
>
>
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